In industrial applications, it is often required to measure the flow
properties of hot and aggressive liquid metals such as aluminum and copper.
Local Lorentz force velocimetry aims to resolve the spatial distribution of
the flow by measuring Lorentz forces at a small permanent magnet brought
into the vicinity of the liquid. In addition, these forces acts on the
fluid and may deflect the flow. The question, on the nature of this
deflection and its impact on the measured forces, will be answered in the
present work by means of analytical and numerical methods. The small magnet
is modeled by a magnetic point dipole that acts on the laminar flow inside
a square duct with insulating walls.Direct numerical simulations are used
to solve the magnetohydrodynamic equations in the quasi-static
approximation for low magnetic Reynolds numbers.The system depends on two
non-dimensional parameters: the Hartmann number Ha and the Reynolds number
Re. Additional influence is given by the geometry, e.\,g. the distance of
the dipole to the surface of the liquid h and the orientation of the
magnetic moment of the dipole. These influences are investigated in
detailed parameter studies. Two power laws are found for the dependency of
the total Lorentz force on the distance.The parameter range considered here
exceeds the range, that can be exploited by recent laboratory experiments.
Nevertheless, the investigations may provide useful hint for the evaluation
of the measured forces. The present study provides for the first time a
detailed parameter study for three-dimensional flow under the influence of
an inhomogeneous localized magnetic field.It opens new perspectives for the
flow manipulation and thus also for flow control.